Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60457 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#60713 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| prime radical | C7×#3058 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C4×C7×#41 ◁ G | |
1878 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,13)(11,12)(14,15)(16,17)(18,27)(19,30)(20,23)(21,25)(22,36)(24,33)(26,35)(28,42)(29,38)(31,44)(32,45)(34,41)(37,46)(39,47)(40,43);(9,12)(13,15)(16,18,21,20)(17,23,25,27)(19,28,32,31)(22,29,35,34)(24,37,39,40)(26,38,36,41)(30,44,45,42)(33,43,47,46);(16,19,22,33,21,32,35,47)(17,24,26,30,25,39,36,45)(18,28,29,43,20,31,34,46)(23,37,38,44,27,40,41,42);(8,10,11,14)(9,13,12,15)(16,20,21,18)(17,23,25,27)(19,31,32,28)(22,34,35,29)(24,37,39,40)(26,38,36,41)(30,44,45,42)(33,46,47,43);(18,20)(23,27)(28,31)(29,34)(37,40)(38,41)(42,44)(43,46)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53701);